1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
zalisa [80]
3 years ago
14

The area of the smallest equilateral triangle with one vertex on each of the sides of the right triangle with side lengths and

img src="https://tex.z-dn.net/?f=%242%5Csqrt%7B3%7D%2C~5%2C%24%20and%20%24%5Csqrt%7B37%7D%2C%24%20" id="TexFormula1" title="$2\sqrt{3},~5,$ and $\sqrt{37},$ " alt="$2\sqrt{3},~5,$ and $\sqrt{37},$ " align="absmiddle" class="latex-formula">as shown, is $\frac{m\sqrt{p}}{n},$ where m, n, and p are positive integers, m and n are relatively prime, and p is not divisible by the square of any prime. What is m + n + p?
Mathematics
2 answers:
Gre4nikov [31]3 years ago
7 0
Set up the given triangle on x-y coordinates with right angle at (0,0). So the two vertices are at (5,0) and (0,2sqrt{x} n]{3})

let (a,0) and (0,b) be two vertices of the<span> equilateral triangle. So the third vertex must be at </span>(\frac{a+\sqrt{3}b}{2} ,  \frac{b+\sqrt{3}a}{2} )

for a pt (x,y) on line sx+ty=1, the minimum of \sqrt{x^{2} + {y^{2} }
equals to \frac{1}{ \sqrt{ s^{2} +  t^{2} } }

smallest value happens at \frac{10 \sqrt{3} }{67}

so area is \frac{75\sqrt{3}}{67}

hence m=75, n=67, p=3
m+n+p = 75+67+3 = 145

dedylja [7]3 years ago
5 0
Hey there,

Your correct answer final answer to this question would be 145.

Hope this helps.

~Jurgen
You might be interested in
a rectangle is made by joining two squares adjacent to each other as shown below. if one squared has an area of 144 squared cent
liberstina [14]

Answer:

Hello! After reading your question I have deduced that the correct answer is 288² cm.

Step-by-step explanation:

The way I came to this conclusion was as follows:

Firstly:

If said rectangle is two squares put side by side (adjacent), then a valid assumption is that both squares are the same size.

This is because all four sides of a square have to be equal.

Thus if the two squares are joined together on one side, then all the other sides of both the squares will be the same length.

Thus both of the squares are going to be the same size, so they will have the same area.

Secondly:

If the area of one square is 144² cm then the area of the other square should also be 144² cm.

Thus if you combine the areas of both the squares, that make up the rectangle, you are left with the area of the rectangle being 288² cm.

I hope this helped!

3 0
2 years ago
Jenny picked 25 roses. she gave away 10 roses. What percent of the roses did Jenny give away?
diamong [38]
Divide 10 by 25, which would get you 4. Move the decimal over two to the left, because you wanted a percentage.

Jenny gave away 40% of the roses.
3 0
3 years ago
Simplify the following:<br> 5 * (7 – 3*4/2)
balu736 [363]

Answer:

5

Step-by-step explanation:

the answer is simply 5 :)

8 0
2 years ago
The triangles below are similar. Find DE. If necessary, round 2 decimal places.
Law Incorporation [45]
We know that the 2 triangles are proportional and are similar so that means there must be a scale factor between the sides of the triangles. To find the D, we need to use the scale factor and multiply it by CD to find DE. The scale factor can be found by dividing 2 similar sides so: EF divided by DG is 5/1.25 which is 4. We can then multiply the scale factor which is 4 by CD so: 3.25 * 4 is 13. DE = 13
7 0
3 years ago
Find the sum of all odd integers between 70 and 120​
Evgen [1.6K]

Answer:

It forms an AP

AP : 71 , 73 , 75 , .................. 119

a = 71

d = 2

a_n= a + (n-1)d

119 = 71 + (n-1)2

n-1 = (119 - 71)/2

n = 24

S_n = n/2 × (a + a_n)

= 24/2 × (71 + 119)

= 12 × 190 = 2280

3 0
3 years ago
Other questions:
  • A carpet square is 9inches what’s the area of the carpet square?
    14·1 answer
  • Lori has 18 new stamps to add to her collection. She displays the stamps on pages of an album in groups of either 3, 6, or 9 sta
    12·2 answers
  • For v=-3i-7j, find the unit vector in the same direction of v, and write your answer as a linear combination of the standard uni
    11·1 answer
  • You drive 150 miles in 3 hours before stopping for 30 minutes to have lunch and gas.  After lunch you travel 100 miles in an hou
    11·1 answer
  • Imagine your typical 7-pound baby. This newborn baby should gain at least roughly 5 ounces per week after the fourth day of life
    9·1 answer
  • Guysss I need help. What's the degree of a 90 degree angle
    11·2 answers
  • Pleas answer my latest 2 questioms thx
    6·1 answer
  • Alvin completely filled his 21-gallon
    14·2 answers
  • A road has a scale of 1:50 000 The length of a road on the map is 8.5cm.Work out the length of the real road in kilometres
    14·1 answer
  • In a woodworking class, you need to make five triangles out of plywood. Each triangle has a height of 6 inches and a base of 14
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!